In the literature, for instance [1]}, [2]}, a class ȍf
relational structures is said to have bounded expansion if the class of their
Gaifman graphs has bounded expansion. It is easy to show that if the class of
Gaifman graphs of structures from h̏as bounded expansion then the
class of adjacency graphs of structures from ȁlso has bounded
expansion. The converse is not true in general. However the converse holds if
the schema is fixed, i.e. ȉs a class of structures all having the same schema.
We refer to [3]} for the simple proofs of these facts.
